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A086759
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Permanent of the Cayley addition table of Z_{n}. a(n) is the permanent of the n X n matrix M_(i,j) = ((i+j) mod n) where i and j range from 0 to n-1.
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2
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0, 1, 9, 164, 5050, 227508, 14064519, 1146668608, 119249333028, 15400125776000, 2417814003691405, 453536611741073664, 100178077459552487070, 25735749696251388478720, 7608415981499790110521875, 2564724413131659780025106432, 977834710569917222742633274504
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OFFSET
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1,3
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LINKS
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EXAMPLE
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a(9) is the permanent of the matrix
0 1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8 0
2 3 4 5 6 7 8 0 1
3 4 5 6 7 8 0 1 2
4 5 6 7 8 0 1 2 3
5 6 7 8 0 1 2 3 4
6 7 8 0 1 2 3 4 5
7 8 0 1 2 3 4 5 6
8 0 1 2 3 4 5 6 7
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MATHEMATICA
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Array[With[{s = Range[0, #]}, Permanent@ Array[RotateLeft[s, #] &, Last@ s + 1, 0]] &, 16, 0] (* Michael De Vlieger, Sep 03 2019 *)
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PROG
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(PARI) permRWNb(a)=n=matsize(a)[1]; if(n==1, return(a[1, 1])); sg=1; in=vectorv(n); x=in; x=a[, n]-sum(j=1, n, a[, j])/2; p=prod(i=1, n, x[i]); for(k=1, 2^(n-1)-1, sg=-sg; j=valuation(k, 2)+1; z=1-2*in[j]; in[j]+=z; x+=z*a[, j]; p+=prod(i=1, n, x[i], sg)); return(2*(2*(n%2)-1)*p) for(n=1, 21, a=matrix(n, n, i, j, ((i+j-2)%n)); print1(permRWNb(a)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007
(PARI) a(n) = matpermanent(matrix(n, n, i, j, (i+j-2) % n)) \\ Stefano Spezia, Oct 25 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 01 2003
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EXTENSIONS
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a(9) from Neven Juric (neven.juric(AT)apis-it.hr), Jul 11 2005
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007
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STATUS
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approved
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